Is the fraction of anthropogenically released

A part of the anthropogenically released

A series of papers argue that the airborne fraction of anthropogenically released

In this paper, we address these statistical issues within the framework of a

The paper is organized as follows. In Sect.

The so-called

The data are available at

While the carbon budget is in principle always balanced for the physical quantities, in the sense that Eq. (

The growth rate in atmospheric

We follow

The airborne fraction and the sink rate are fundamentally different quantities.
The airborne fraction AF

In this section, we consider several models for the data-generating process behind observations of the objects of interest defined in Sect.

Our baseline model is the local linear trend (LLT) model. For a univariate time series

The local linear trend model can be cast in the state-space system Eq. (

It follows immediately from Eq. (

We consider our baseline local linear trend model of Sect.

Table

Univariate analysis of the airborne fraction.

We report parameter estimates for the standard deviations

The state-space system allows both measures for the airborne fraction, AF

Multivariate analysis of the airborne fraction.

We report parameter estimates for the standard deviations

Since the two quantities in Eq. (

Estimated trend

In this section, we analyse the

The basic (univariate) local linear trend model for each of these objects is then given by

Univariate analysis of the

We report parameter estimates for the standard deviations

Analogously to the airborne fraction above, these data can be put in a joint uninformed system with two different trend components, and we have

Multivariate analysis of the

We report parameter estimates for the standard deviations

Finally, we consider the state-space system that imposes a common trend for both time series,

The state-space system is also well-suited for forecasting; see

It is important to recognize that the validity of these forecasts are conditional on the assumption that the sink rate,

Estimated trend

The blue solid line represents the data, while the red solid line represents the point forecasts from the Kalman filter with the unknown parameters estimated by maximum likelihood. The dashed red lines are

We may conclude from the analysis in the previous section that
the combined (land plus ocean) sink rate appears to be decreasing.
To investigate this finding in more detail, we study two alternative models, which consider the two sink variables separately.
The first model specifies local linear trends for ocean and land sink rates, i.e.

The estimation results for these two model specifications are presented in Table

Analysis of ocean and land sink rates.

We report parameter estimates for standard deviations

Previous studies of the airborne fraction and the

In some of the uninformed models (cf. Table

Several studies have highlighted the need for accounting for noise in measurements of climate-related data

Why do we find statistical evidence of a decreasing

What are possible physical explanations for the apparent decrease in the sink rate?

It is possible that the analyses conducted above are influenced by external natural events such as the El Niño–Southern Oscillation (ENSO), volcanic eruptions, and the like

This paper considers data recorded at a yearly frequency, while many of the previous studies of the airborne fraction and the sink rate use monthly data. The advantage of using monthly data is obvious: more observations. However, there are also some disadvantages. For instance, while the

We have argued that the state-space system can be a useful approach for analysing possible trends in the airborne fraction of anthropogenically released

We estimate a positive, yet statistically insignificant, slope in the data for the airborne fraction. Using two alternative time series for the sink rate and imposing a common trend, we obtain a significantly negative deterministic trend.
Our analyses support the conclusions as set out by

Finally, there is tentative evidence that the decrease in the sink rate is mainly driven by a weakening uptake in the land sink. This could be the result of non-linearities in the response of the terrestrial carbon sink to the level of atmospheric concentrations of

The data used in this paper are available at the website of the Global Carbon Project (

In this Appendix, we argue that the levels of atmospheric concentrations of

From Eq. (

The precise relationship between

Thus, if

The supplement related to this article is available online at:

MB, EH, and SJK studied the data and discussed possible models. MB conceived of the idea to focus on the airborne fraction and the sink rate. MB, EH, and SJK went through the modelling cycle for these objects of interest. MB and SJK ran the estimations in MATLAB and OX, respectively. MB, EH, and SJK discussed the results and wrote the paper jointly.

The author declares that there is no conflict of interest.

We would like to thank Corinne Le Quéré for permission to use the data set of

This research has been supported by the Independent Research Fund Denmark (grant no. 7015-00018B).

This paper was edited by Laurent Bopp and reviewed by two anonymous referees.